Question

if 5 cards are dealt, find the probability of getting 4 of a kind.

Answer 1

A hand containing four cards of the same value, such as King(spade,hearts,diamond,clubs) are called 4 of a kind.

A pack of cards contains 52 cards.

Here we select 5 cards out of the 52 cards.

So we can choose the 5 cards in ways

There are total 13 types of four of a kind cards. They are { Ace, 2, 3, 4, 5, 6, 7, 8, 9, 10, Jack, Queen, King }. Among those 13 types we can choose one type of (4 of a kind) cards in ways.

The 5th card can be chosen from the remaining (52-4)=48 cards in ways.

If 5 cards are dealt, the probability of getting 4 of a kind is :

Answer : The required prbability is 0.00024 (upto 5 decimal point)